Snap-Stabilization in Message-Passing Systems

In this paper, we tackle the open problem of snap-stabilization in message-passing systems. Snap-stabilization is a nice approach to design protocols that withstand transient faults. Compared to the well-known self-stabilizing approach, snap-stabilization guarantees that the effect of faults is contained immediately after faults cease to occur. Our contribution is twofold: we show that (1) snap-stabilization is impossible for a wide class of problems if we consider networks with finite yet unbounded channel capacity; (2) snap-stabilization becomes possible in the same setting if we assume bounded-capacity channels. We propose three snap-stabilizing protocols working in fully-connected networks. Our work opens exciting new research perspectives, as it enables the snap-stabilizing paradigm to be implemented in actual networks

Trade-off between Time, Space, and Workload: the case of the Self-stabilizing Unison

We present a self-stabilizing algorithm for the (asynchronous) unison problem which achieves an efficient trade-off between time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works in anonymous networks in which even local ports are unlabeled. It makes no assumption on the daemon and thus stabilizes under the weakest one: the distributed unfair daemon. In a $n$-node network of diameter $D$ and assuming a period $B \geq 2D+2$, our algorithm only requires $O(\log B)$ bits per node to achieve full polynomiality as it stabilizes in at most $2D-2$ rounds and $O(\min(n^2B, n^3))$ moves. In particular and to the best of our knowledge, it is the first self-stabilizing unison for arbitrary anonymous networks achieving an asymptotically optimal stabilization time in rounds using a bounded memory at each node. Finally, we show that our solution allows to efficiently simulate synchronous self-stabilizing algorithms in an asynchronous environment. This provides a new state-of-the-art algorithm solving both the leader election and the spanning tree construction problem in any identified connected network which, to the best of our knowledge, beat all existing solutions of the literature.Comment: arXiv admin note: substantial text overlap with arXiv:2307.0663

Automated Analysis and Optimization of Distributed Self-Stabilizing Algorithms

Self-stabilization [2] is a versatile technique for recovery from erroneous behavior due to transient faults or wrong initialization. A system is self-stabilizing if (1) starting from an arbitrary initial state it can automatically reach a set of legitimate states in a finite number of steps and (2) it remains in legitimate states in the absence of faults. Weak-stabilization [3] and probabilistic-stabilization [4] were later introduced in the literature to deal with resource consumption of self-stabilizing algorithms and impossibility results. Since the system perturbed by fault may deviate from correct behavior for a finite amount of time, it is paramount to minimize this time as much as possible, especially in the domain of robotics and networking. This type of fault tolerance is called non-masking because the faulty behavior is not completely masked from the user [1]. Designing correct stabilizing algorithms can be tedious. Designing such algorithms that satisfy certain average recovery time constraints (e.g., for performance guarantees) adds further complications to this process. Therefore, developing an automatic technique that takes as input the specification of the desired system, and synthesizes as output a stabilizing algorithm with minimum (or other upper bound) average recovery time is useful and challenging. In this thesis, our main focus is on designing automated techniques to optimize the average recovery time of stabilizing systems using model checking and synthesis techniques. First, we prove that synthesizing weak-stabilizing distributed programs from scratch and repairing stabilizing algorithms with average recovery time constraints are NP-complete in the state-space of the program. To cope with this complexity, we propose a polynomial-time heuristic that compared to existing stabilizing algorithms, provides lower average recovery time for many of our case studies. Second, we study the problem of fine tuning of probabilistic-stabilizing systems to improve their performance. We take advantage of the two properties of self-stabilizing algorithms to model them as absorbing discrete-time Markov chains. This will reduce the computation of average recovery time to finding the weighted sum of elements in the inverse of a matrix. Finally, we study the impact of scheduling policies on recovery time of stabilizing systems. We, in particular, propose a method to augment self-stabilizing programs with k-central and k-bounded schedulers to study dierent factors, such as geographical distance of processes and the achievable level of parallelism